# Mechanical Engineering Dimensionless Numbers

Notations and units:

Re = Reynolds Number, Nu = Nusselt Number, Pr = Prandtl Number, Gr = Grashof Number, µ = Dynamic viscosity

$\nu$ = Kinematic viscosity, $L_{ch}$ = Diameter or Length based on the environment, C = Specific heat, $\mu_{f}$ = Coefficient of friction, K = Thermal conductivity, h = Heat transfer coefficient, g = acceleration due to gravity, β = Coefficient of thermal expansion, T = Temperature

Units of the notations are in SI units.

1.Stanton Number = Heat transferred into fluid / Thermal capacity of the fluid

Stanton Number = $\frac{Nu}{Re \times Pr}$ = $\frac{\mu_{f}}{2 \times (Pr)^{2/3}}$

2.Schmidt Number = Momentum diffusivity or kinematic viscosity / Mass diffusivity

3.Sherwood Number = Convective mass transfer / Diffusion mass transfer

4.Lewis Number = Thermal diffusivity / Mass diffusivity

5.Peclet Number = Convective heat transfer / Conductive heat transfer

6.Reynolds Number = Inertia force / Viscous force

Reynolds Number = $\frac{Velocity(V) \times L_{ch}}{\nu}$

$\nu$ = dynamic viscosity / mass density

7.Euler Number = inertia force / pressure force

8.Prandtl Number = diffusion of momentum / diffusion of heat

Prandtl Number = $\frac{\mu\times C}{K}$

Prandtl Number = Velocity boundary layer thickness / Thermal boundary layer thickness

9.Nusselt Number = Conduction resistance of the fluid / Convection resistance of the fluid

Nusselt Number = $\frac{h\times L_{ch}}{K}$

10.Grashof Number = (buoyancy force / viscous force) x Re

Grashof Number = $\frac{g\beta(T_{surface}-T_{fluid})L_{ch}^{3}}{\nu^{3}}$

11.Cauchy Number = inertia force / elastic force

12.Fourier Number = ability of the solid to conduct energy / ability to store energy

13.Rayleigh Number = Gr x Pr

14.Froude Number = inertia force / gravity force

15.Weber Number = inertia force / surface tension force

16.Mach Number = velocity of the stream / velocity of the sound

17.Biot Number = internal conductive resistance of the solid / convective resistance of the fluid

Biot Number = $\frac{h\times L_{ch}}{K}$